Crystal Made Exclusively of Electrons – Wigner ‘Holy Grail’ Crystals Seen for the First Time

Crystal Wigner

An electron wigner crystal (red) inside a semiconductor material (blue / gray). Credit: ETH Zurich

Researchers at ETH Zurich have successfully observed a crystal made up entirely of electrons. Such Wigner crystals were already predicted almost ninety years ago, but could only be observed directly in a semiconductor material now.

Crystals have fascinated people throughout the ages. Who has never admired the intricate patterns of a snowflake or the perfectly symmetrical surfaces of a rock crystal? The magic does not stop even if we know that all this results from a simple game of attraction and repulsion between atoms and electrons. A team of researchers led by Ataç Imamoğlu, professor at the Institute for Quantum Electronics at ETH Zurich, has now produced a very special crystal. Unlike normal crystals, it is made up exclusively of electrons. In doing so, they confirmed a theoretical prediction that was made almost ninety years ago and has since been seen as some kind of holy grail of condensed matter physics. Their results were recently published in the scientific journal Nature.

A decades-old prediction

“What got us excited about this problem was its simplicity,” says Imamoğlu. Already in 1934, Eugene Wigner, one of the founders of the theory of symmetries in quantum mechanics, showed that the electrons of a material could theoretically organize themselves into regular patterns, similar to crystals, due to their mutual electrical repulsion. . The reasoning behind this is quite simple: if the energy of the electrical repulsion between electrons is greater than their energy of motion, they will arrange such that their total energy is as small as possible.

For several decades, however, this prediction remained purely theoretical, as these “Wigner crystals” can only form under extreme conditions such as low temperatures and a very small number of free electrons in the material. This is in part because electrons are several thousand times lighter than atoms, which means that their energy of motion in a regular arrangement is usually much greater than electrostatic energy due to the interaction between them. electrons.

Electrons in an airplane

To overcome these obstacles, Imamoğlu and his collaborators chose an ultra-thin layer of molybdenum diselenide, a semiconductor material, only one atom thick and in which, therefore, electrons cannot move. that in a plane. The researchers were able to vary the number of free electrons by applying a voltage to two transparent graphene electrodes, between which the semiconductor is sandwiched. Based on theoretical considerations, the electrical properties of molybdenum diselenide should favor the formation of a Wigner crystal – provided the entire apparatus is cooled to a few degrees above absolute zero of minus 273.15 degrees Celsius.

Electronic Liquid Wigner Crystal

Electrons in a material generally behave like a disordered liquid (left), but can form a regular Wigner crystal (right) under particular conditions. Credit: ETH Zurich

However, producing a Wigner crystal is not enough. “The next problem was to demonstrate that we actually had Wigner crystals in our device,” says Tomasz Smoleński, who is the lead author of the publication and works as a post-doctoral fellow in Imamoğlu’s lab. The separation between electrons has been calculated to be around 20 nanometers, which is around thirty times smaller than the wavelength of visible light and therefore impossible to resolve even with the best microscopes.

Exciton detection

Using a trick, the physicists managed to make visible the regular arrangement of electrons despite this small separation in the crystal lattice. To do this, they used light of a particular frequency to excite what are called excitons in the semiconductor layer. Excitons are pairs of electrons and “holes” that result from a missing electron in an energy level of the material. The precise frequency of light for creating such excitons and the speed at which they move depends both on the properties of the material and on the interaction with other electrons in the material – with a Wigner crystal, for example. .

The periodic arrangement of electrons in the crystal gives rise to an effect that can sometimes be seen on television. When a bicycle or a car goes faster and faster, above a certain speed, the wheels seem to stop and then turn in the opposite direction. This is because the camera takes a snapshot of the wheel every 40 milliseconds. If during this time the evenly spaced spokes of the wheel have moved exactly the distance between the spokes, the wheel appears to no longer turn. Likewise, in the presence of a Wigner crystal, the moving excitons appear stationary provided that they move at a certain speed determined by the separation of electrons in the crystal lattice.

First direct observation

“A group of theoretical physicists led by Eugene Demler of Harvard University, who is moving to ETH this year, had theoretically calculated how this effect should appear in the observed excitation frequencies of the excitons – and that’s exactly what we have observed in the laboratory, ”says Imamoglu. Unlike previous experiments based on planar semiconductors, in which Wigner crystals were observed indirectly by current measurements, this is a direct confirmation of the arrangement. regularity of electrons in the crystal.In the future, with their new method, Imamoğlu and his colleagues hope to study exactly how Wigner crystals are formed from a disordered “liquid” of electrons.

Reference: “Signatures of Wigner crystal of electrons in a monolayer semiconductor” by Tomasz Smoleński, Pavel E. Dolgirev, Clemens Kuhlenkamp, ​​Alexander Popert, Yuya Shimazaki, Patrick Back, Xiaobo Lu, Martin Kroner, Kenji Watanabe, Takashi Taniguchi, Ilya Esterlis, Eugene Demler and Ataç Imamoğlu, June 30, 2021, Nature.
DOI: 10.1038 / s41586-021-03590-4